A matrix-free implicit iterative solver for compressible flow problems. (English) Zbl 0838.76040

Johan, Z.; Hughes, T. J. R.; Shakib, F.

Rend. Semin. Mat., Torino, Spec. Iss., 141-161 (1991).

Summary: A procedure for solving nonlinear time-marching problems is presented. The nonsymmetric systems of equations arising from Newton-type linearizations are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

generalized minimal residual algorithm; time-marching problems; Newton-type linearizations; automatic time-increment control strategy